Many problems from the fields of accelerator physics and beam theory can be formulated as optimization problems and thus can benefit from modern optimization techniques. However, the use of such techniques in these fields is so far rather limited. Relatively new and actively developed Evolutionary Algorithms (EAs) for optimization possess many attractive features such as: ease of implementation, modest requirements on the objective function, good tolerance to noise, robustness and the ability to efficiently perform a global search. These make them the tool of choice for many design and optimization problems. We present several different problems of accelerator design and demonstrate how they can be treated by EAs.